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The evolution of the Australian monsoon in relation to high-latitude temperature fluctuations over the last termination remains highly enigmatic. Here we integrate high-resolution riverine runoff and dust proxy data from X-ray fluorescence scanner measurements in four well-dated sediment cores, forming a NE-SW transect across the Timor Sea. Our records reveal that the development of the Australian monsoon closely followed the deglacial warming history of Antarctica. A minimum in riverine runoff documents dry conditions throughout the region during the Antarctic Cold Reversal (15-12.9 ka). Massive intensification of the monsoon coincided with Southern Hemisphere warming and intensified greenhouse forcing over Australia during the atmospheric CO2 rise at 12.9-10 ka. We relate the earlier onset of the monsoon in the Timor Strait (13.4 ka) to regional changes in landmass exposure during deglacial sea-level rise. A return to dryer conditions occurred between 8.1 and 7.3 ka following the early Holocene runoff maximum.

Observations show that summer rainfall over large parts of South Asia has declined over the past five to six decades. It remains unclear, however, whether this trend is due to natural variability or increased anthropogenic aerosol loading over South Asia. Here we use stable oxygen isotopes in speleothems from northern India to reconstruct variations in Indian monsoon rainfall over the last two millennia. We find that within the long-term context of our record, the current drying trend is not outside the envelope of monsoon’s oscillatory variability, albeit at the lower edge of this variance. Furthermore, the magnitude of multi-decadal oscillatory variability in monsoon rainfall inferred from our proxy record is comparable to model estimates of anthropogenic-forced trends of mean monsoon rainfall in the 21st century under various emission scenarios. Our results suggest that anthropogenicforced changes in monsoon rainfall will remain difficult to detect against a backdrop of large natural variability

The evolution of the Australian monsoon in relation to high-latitude temperature fluctuations over the last termination remains highly enigmatic. Here we integrate high-resolution riverine runoff and dust proxy data from X-ray fluorescence scanner measurements in four well-dated sediment cores, forming a NE–SW transect across the Timor Sea. Our records reveal that the development of the Australian monsoon closely followed the deglacial warming history of Antarctica. A minimum in riverine runoff documents dry conditions throughout the region during the Antarctic Cold Reversal (15–12.9 ka). Massive intensification of the monsoon coincided with Southern Hemisphere warming and intensified greenhouse forcing over Australia during the atmospheric CO2 rise at 12.9–10 ka. We relate the earlier onset of the monsoon in the Timor Strait (13.4 ka) to regional changes in landmass exposure during deglacial sea-level rise. A return to dryer conditions occurred between 8.1 and 7.3 ka following the early Holocene runoff maximum.

Tropical south-western Pacific temperatures are of vital importance to the Great Barrier Reef (GBR), but the role of sea surface temperatures (SSTs) in the growth of the GBR since the Last Glacial Maximum remains largely unknown. Here we present records of Sr/Ca and d18O for Last Glacial Maximum and deglacial corals that show a considerably steeper meridional SST gradient than the present day in the central GBR. We find a 1–2 °C larger temperature decrease between 17° and 20°S about 20,000 to 13,000 years ago. The result is best explained by the northward expansion of cooler subtropical waters due to a weakening of the South Pacific gyre and East Australian Current. Our findings indicate that the GBR experienced substantial meridional temperature change during the last deglaciation, and serve to explain anomalous deglacial drying of northeastern Australia. Overall, the GBR developed through significant SST change and may be more resilient than previously thought.

Whereas millennial to submillennial climate variability has been identified during the current interglacial period, past interglacial variability features remain poorly explored because of lacking data at sufficient temporal resolutions. Here we present new deuterium data from the EPICA Dome C ice core, documenting at decadal resolution temperature changes occurring over the East Antarctic plateau during the warmer-than-today last interglacial. Expanding previous evidence of instabilities during the last interglacial, multicentennial subevents are identified and labeled for the first time in a past interglacial context. A variance analysis further reveals two major climatic features. First, an increase in variability is detected prior to the glacial inception, as already observed at the end of Marine Isotopic Stage 11 in the same core. Second, the overall variance level is systematically higher during the last interglacial than during the current one, suggesting that a warmer East Antarctic climate may also be more variable.

Estimation of Pearson’s correlation coefficient between two time series, in the evaluation of the influences of one time-dependent variable on another, is an often used statistical method in climate sciences. Data properties common to climate time series, namely non-normal distributional shape, serial correlation, and small data sizes, call for advanced, robust methods to estimate accurate confidence intervals to support the correlation point estimate. Bootstrap confidence intervals are estimated in the Fortran 90 program PearsonT (Mudelsee, Math Geol 35(6):651–665, 2003), where themain intention is to obtain accurate confidence intervals for correlation coefficients between two time series by taking the serial dependence of the data-generating process into account. However, Monte Carlo experiments show that the coverage accuracy of the confidence intervals for smaller data sizes can be substantially improved. In the present paper, the existing program is adapted into a new version, called PearsonT3, by calibrating the confidence interval to increase the coverage accuracy. Calibration is a bootstrap resampling technique that performs a second bootstrap loop (it resamples from the bootstrap resamples). It offers, like the non-calibrated bootstrap confidence intervals, robustness against the data distribution. Pairwise moving block bootstrap resampling is used to preserve the serial dependence of both time series. The calibration is applied to standard error-based bootstrap Student’s t confidence intervals. The performance of the calibrated confidence interval is examined with Monte Carlo simulations and compared with the performance of confidence intervalswithout calibration.

The climate during the Cenozoic era changed in several steps from ice-free poles and warm conditions to ice-covered poles and cold conditions. Since the 1950s, a body of information on ice volume and temperature changes has been built up predominantly on the basis of measurements of the oxygen isotopic composition of shells of benthic foraminifera collected from marine sediment cores. The statistical methodology of time series analysis has also evolved, allowing more information to be extracted from these records. Here we provide a comprehensive view of Cenozoic climate evolution by means of a coherent and systematic application of time series analytical tools to each record from a compilation spanning the interval from 4 to 61 Myr ago. We quantitatively describe several prominent features of the oxygen isotope record, taking into account the various sources of uncertainty (including measurement, proxy noise, and dating errors). The estimated transition times and amplitudes allow us to assess causal climatological-tectonic influences on the following known features of the Cenozoic oxygen isotopic record: Paleocene-Eocene Thermal Maximum, Eocene-Oligocene Transition, Oligocene-Miocene Boundary, and the Middle Miocene Climate Optimum. We further describe and causally interpret the following features: Paleocene-Eocene warming trend, the two-step, long-term Eocene cooling, and the changes within the most recent interval (Miocene-Pliocene). We review the scope and methods of constructing Cenozoic stacks of benthic oxygen isotope records and present two new latitudinal stacks, which capture besides global ice volume also bottom water temperatures at low (less than 30°) and high latitudes. This review concludes with an identification of future directions for data collection, statistical method development, and climate modeling.

Studying the climate dynamics of past interglacials (IGs) may help to better assess the anthropogenically influenced dynamics of the current IG, the Holocene. We select IG sections from the longest ice core archive, EPICA Dome C (EDC), which covers the past 800 thousand years, and study as well several long, high-resolution marine sediment records. We analyze records of Antarctic temperature, radiative forcing (greenhouse gases and other factors), and sea-surface temperature (SST). Change-point regressions inform about longer-term climate changes and trends within IGs. Comparing trends in temperature with trends in forcing allows inference of longer-term IG climate sensitivities. Results from many records indicate deviations from a “Holocene climate optimum”. IG sensitivities are found to be comparable to estimates for the instrumental period; warming or cooling phases during Marine Isotope Stage (MIS) 5 or 11 do not show significant differences in climate sensitivity.

There are a number of clear examples in the instrumental period where positive El Niño events were coincident with a severely weakened summer monsoon over India (ISM). ENSO's influence on the Indian Monsoon has therefore remained the centerpiece of various predictive schemes of ISM rainfall for over a century. The teleconnection between the monsoon and ENSO has undergone a protracted weakening since the late 1980's suggesting the strength of ENSO's influence on the monsoon may vary considerably on multidecadal timescales. The recent weakening has specifically prompted questions as to whether this shift represents a natural mode of climate variability or a fundamental change in ENSO and/or ISM dynamics due to anthropogenic warming. The brevity of empirical observations and large systematic errors in the representation of these two systems in state-of-the-art general circulation models hamper efforts to reliably assess the low frequency nature of this dynamical coupling under varying climate forcings. Here we place the 20th century ENSO-Monsoon relationship in a millennial context by assessing the phase angle between the two systems across the time spectrum using a continuous tree-ring ENSO reconstruction from North America and a speleothem oxygen isotope (δ18O) based reconstruction of the ISM. The results suggest that in the high-frequency domain (≤ 15 yr), El Niño (La Niña) events persistently lead to a weakened (strengthened) monsoon consistent with the observed relationship between the two systems during the instrumental period. However, in the low frequency domain (≥ 60 yr), periods of strong monsoon are, in general, coincident with periods of enhanced ENSO variance. This relationship is opposite to which would be predicted dynamically and leads us to conclude that ENSO is not pacing the prominent multidecadal variability that has characterized the ISM over the last millennium.

We introduce a technique of time series analysis, potential forecasting, which is based on dynamical propagation of the probability density of time series. We employ polynomial coefficients of the orthogonal approximation of the empirical probability distribution and extrapolate them in order to forecast the future probability distribution of data. The method is tested on artificial data, used for hindcasting observed climate data, and then applied to forecast Arctic sea-ice time series. The proposed methodology completes a framework for ‘potential analysis’ of tipping points which altogether serves anticipating, detecting and forecasting nonlinear changes including bifurcations using several independent techniques of time series analysis. Although being applied to climatological series in the present paper, the method is very general and can be used to forecast dynamics in time series of any origin.

Holocene climate was characterised by variability on multi-centennial to multi-decadal time scales. In central Europe, these fluctuations were most pronounced during winter. Here we present a new record of past winter climate variability for the last 10.8 ka based on four speleothems from Bunker Cave, Western Germany. Due to its central European location, the cave site is particularly well suited to record changes in precipitation and temperature in response to changes in the North Atlantic realm. We present high resolution records of δ18O, δ13C values and Mg/Ca ratios. We attribute changes in the Mg/Ca ratio to variations in the meteoric precipitation. The stable C isotope composition of the speleothems most likely reflects changes in vegetation and precipitation and variations in the δ18O signal are interpreted as variations in meteoric precipitation and temperature. We found cold and dry periods between 9 and 7 ka, 6.5 and 5.5 ka, 4 and 3 ka as well as between 0.7 to 0.2 ka. The proxy signals in our stalagmites compare well with other isotope records and, thus, seem representative for central European Holocene climate variability. The prominent 8.2 ka event and the Little Ice Age cold events are both recorded in the Bunker cave record. However, these events show a contrasting relationship between climate and δ18O, which is explained by different causes underlying the two climate anomalies. Whereas the Little Ice Age is attributed to a pronounced negative phase of the North Atlantic Oscillation, the 8.2 ka event was triggered by cooler conditions in the North Atlantic due to a slowdown of the Thermohaline Circulation.

A fundamental problem in paleoclimatology is to take fully into account the various error sources when examining proxy records with quantitative methods of statistical time series analysis. Records from dated climate archives such as speleothems add extra uncertainty from the age determination to the other sources that consist in measurement and proxy errors. This paper examines three stalagmite time series of oxygen isotopic composition (δ18O) from two caves in western Germany, the series AH-1 from the Atta Cave and the series Bu1 and Bu4 from the Bunker Cave. These records carry regional information about past changes in winter precipitation and temperature. U/Th and radiocarbon dating reveals that they cover the later part of the Holocene, the past 8.6 thousand years (ka). We analyse centennial- to millennial-scale climate trends by means of nonparametric Gasser–Müller kernel regression. Error bands around fitted trend curves are determined by combining (1) block bootstrap resampling to preserve noise properties (shape, autocorrelation) of the δ18O residuals and (2) timescale simulations (models StalAge and iscam). The timescale error influences on centennial- to millennial-scale trend estimation are not excessively large. We find a "mid-Holocene climate double-swing", from warm to cold to warm winter conditions (6.5 ka to 6.0 ka to 5.1 ka), with warm–cold amplitudes of around 0.5‰ δ18O; this finding is documented by all three records with high confidence. We also quantify the Medieval Warm Period (MWP), the Little Ice Age (LIA) and the current warmth. Our analyses cannot unequivocally support the conclusion that current regional winter climate is warmer than that during the MWP

Trend describes time-dependence in the first moment of a stochastic process, and correlation measures the linear relation between two random variables. Accurately estimating the trend and correlation, including uncertainties, from climate time series data in the uni- and bivariate domain, respectively, allows first-order insights into the geophysical process that generated the data. Timescale errors, ubiquitious in paleoclimatology, where archives are sampled for proxy measurements and dated, poses a problem to the estimation. Statistical science and the various applied research fields, including geophysics, have almost completely ignored this problem due to its theoretical almost-intractability. However, computational adaptations or replacements of traditional error formulas have become technically feasible. This contribution gives a short overview of such an adaptation package, bootstrap resampling combined with parametric timescale simulation. We study linear regression, parametric change-point models and nonparametric smoothing for trend estimation. We introduce pairwise-moving block bootstrap resampling for correlation estimation. Both methods share robustness against autocorrelation and non-Gaussian distributional shape. We shortly touch computing-intensive calibration of bootstrap confidence intervals and consider options to parallelize the related computer code. Following examples serve not only to illustrate the methods but tell own climate stories: (1) the search for climate drivers of the Agulhas Current on recent timescales, (2) the comparison of three stalagmite-based proxy series of regional, western German climate over the later part of the Holocene, and (3) trends and transitions in benthic oxygen isotope time series from the Cenozoic. Financial support by Deutsche Forschungsgemeinschaft (FOR 668, FOR 1070, MU 1595/4-1) and the European Commission (MC ITN 238512, MC ITN 289447) is acknowledged.

Here we present high-resolution stable isotope and lamina thickness profiles as well as radiocarbon data for the Holocene stalagmite ER 76 from Grotta di Ernesto (north-eastern Italy), which was dated by combined U-series dating and lamina counting. ER 76 grew between 8 ka (thousands of years before 2000 AD) and today, with a hiatus from 2.6 to 0.4 ka. Data from nine meteorological stations in Trentino show a significant influence of the North Atlantic Oscillation (NAO) on winter temperature and precipitation in the cave region. Spectral analysis of the stable isotope signals of ER 76 reveals significant peaks at periods of 110, 60–70, 40–50, 32–37 and around 25 a. Except for the cycle between 32 and 37 a all periodicities have corresponding peaks in power spectra of solar variability, and the 25-a cycle may correspond to NAO variability. This suggests that climate variability in northern Italy was influenced by both solar activity and the NAO during the Holocene. Six periods of warm winter climate in the cave region were identified. These are centred at 7.9, 7.4, 6.5, 5.5, 4.9 and 3.7 ka, and their duration ranges from 100 to 400 a. The two oldest warm phases coincide with the deposition of sapropel S1 in the Mediterranean Sea indicating that the climate in the cave region was influenced by this prominent pluvial phase in the Mediterranean area. For the younger warm phases it is difficult to establish a supra-regional climate pattern, and some of them may, thus, reflect regional climate variability. This highlights the complexity of regional and supra-regional scale Holocene climate patterns.

The annual temperatures recorded for the last two centuries in fifteen european stations around the Alps are analyzed. They show a global warming whose growth rate is not however constant in time. An analysis based on linear Arima models does not provide accurate results. Thus, we propose threshold nonlinear nonstationary models based on several regimes both in time and in levels. Such models fit all series satisfactorily, allow a closer description of the temperature changes evolution, and help to discover the essential differences in the behavior of the different stations.

Paleoclimate is the climate in the geologic past. Paleoclimatic information comes from natural archives (e.g., speleothems, marine sediment cores) and measurements of indicator or proxy variables (e.g., oxygen isotopes), while the time information comes from dated samples of the archive. Since climate archives exhibit growth changes over time, the resulting time series is unevenly spaced. Since the dating exhibits measurement error, the resulting timescale is uncertain. In addition to these two paleoclimate-specific challenges (uneven spacing, uncertain timescale), two challenges more common to statistical science appear (non-normal distributional shape, autocorrelation). We have previously shown [Mudelsee 2010, Climate Time Series Analysis, Springer; www.manfredmudelsee.com/book ] that the bootstrap resampling approach is able to meet these four challenges. This talk illustrates various ingredients of the bootstrap adaption to paleoclimate time series analysis, namely the AR(1) process for uneven spacing, (pairwise) moving-block resampling, parametric timescale simulations, confidence interval construction and Monte Carlo tests. We exemplify our bootstrap adaptation on two estimation problems. The first is spectrum estimation and the search for solar cycles in proxy records of the Indian summer monsoon covering the past 10000 years. The second example comes from the GATEWAYS project (Multi-level assessment of ocean-climate dynamics: A gateway to interdisciplinary training and analysis) and deals with correlation estimation on paleoceanographic time series from the Agulhas region,south of South Africa. Supporting grants: This work is supported by the European Commission via the Marie Curie Initial Training Network GATEWAYS (project number 238512) under the Seventh Framework Programme. Key words: Bootstrap, Climate, Correlation, Spectrum, Time Series

Various climatic processes are thought to evolve as rapid, shift-like events, which points at the presence of nonlinear dynamics. Time series analysis of nonlinear processes, however, is not trivial, for example, because of the difficulty in coming up with a realistic random process as a viable null hypothesis. In this methodology paper we construct a basic two-parameter process of shift-like excursions in an excitable system with a threshold. We demonstrate that this stochastic process, in comparison with a specific one-parameter process, can better reproduce main features of the waiting time histogram of abrupt glacial climate events, the Dansgaard-Oeschger events, as seen in two paleoclimatic proxy records, the North Greenland Ice core Project (NGRIP) ice core and the Sofular stalagmite δ18O records. We use the two-parameter process to test some arguments that were proposed in the ongoing discussion of a possible solar role in triggering Dansgaard-Oeschger events. Using our approach, we suggest for future studies to generate time series of random events which can serve as a more plausible null hypothesis for Monte Carlo based statistical tests on the regularity of shift-like processes such as Dansgaard-Oeschger events.

The “internally” generated intraseasonal variability of the Indian Summer Monsoon is characterized by intermittent periods of enhanced (“active”) and deficient (“break”) precipitation, which produce a quasi east-west precipitation dipole over the Indian subcontinent. Here we present multicentennial-length and near annually-resolved reconstructions of monsoon precipitation, inferred from absolute-dated and instrumentally calibrated speleothem oxygen isotope records from regions (central and northeast India) that have diametric responses to active-break monsoon circulation patterns. On centennial timescales (AD 1400–2008), precipitation variability from these two regions exhibit opposing behavior, oscillating between periods with a persistently “active-dominated” (AD ∼1700 to 2007) and a “break-dominated” (AD 1400 to ∼1700) regime. The switch between these regimes occurs abruptly (within decades) at a time (AD ∼ 1650–1700) when a proxy record of upwelling intensity from the Arabian Sea suggest an abrupt increase in the monsoon winds. On the basis of these observations, we hypothesize that the frequency distribution of active-break periods varies on centennial timescales, implying a leading role of internal dynamics in governing the ISM response to slowly-evolving changes in the external boundary conditions.